Partial implementation of Zygote AD with symbolic indexing

[contradict]

Symbolic indexing of state and observed variables. Time index must be specified for observed symbols.

This is a rebase and fixup of https://github.com/lamorton/scimlbase.jl/tree/zygote_rules

[codecov[bot]]

Codecov Report

Merging #479 (d5d5e37) into master (cce1ce0) will increase coverage by 3.08%. The diff coverage is 30.00%.

@@            Coverage Diff             @@
##           master     #479      +/-   ##
==========================================
+ Coverage   53.73%   56.82%   +3.08%     
==========================================
  Files          47       50       +3     
  Lines        3584     3657      +73     
==========================================
+ Hits         1926     2078     +152     
+ Misses       1658     1579      -79     

Files Changed	Coverage Δ
src/SciMLBase.jl	71.42% <ø> (ø)
src/solutions/chainrules.jl	0.00% <0.00%> (ø)
src/solutions/zygote.jl	46.15% <46.15%> (ø)
ext/ZygoteExt.jl	50.00% <50.00%> (ø)

... and 9 files with indirect coverage changes

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[ChrisRackauckas]

Alright cool this looks good to go if tests pass. I hope we can get sol[sym] working ASAP afterwards since that's probably the most commonly used call, but at least there's a workaround for now.

[contradict]

Oh, it fails on 1.6 since package extensions don't exist yet. Should I skip the tests on 1.6 or is there a workaround to get the extensions to load?

[ChrisRackauckas]

Just skip v1.6. We're getting close to dropping it (please LTS come soon).

[ChrisRackauckas]

https://github.com/SciML/SciMLBase.jl/actions/runs/5837232743/job/15843572165?pr=479#step:6:975